ALBERT

Description: Glacial isostatic adjustment is largely governed by the rheological properties of the Earth's mantle. Large mass redistributions in the ocean–cryosphere system and the subsequent response of the viscoelastic Earth have led to dramatic sea level changes in the past. This process is ongoing, and in order to understand and predict current and future sea level changes, the knowledge of mantle properties such as viscosity is essential. In this study, we present a method to obtain estimates of mantle viscosities by the assimilation of relative sea level rates of change into a viscoelastic model of the lithosphere and mantle. We set up a particle filter with probabilistic resampling. In an identical twin experiment, we show that mantle viscosities can be recovered in a glacial isostatic adjustment model of a simple three-layer Earth structure consisting of an elastic lithosphere and two mantle layers of different viscosity. We investigate the ensemble behaviour on different parameters in the following three set-ups: (1) global observations data set since last glacial maximum with different ensemble initialisations and observation uncertainties, (2) regional observations from Fennoscandia or Laurentide/Greenland only, and (3) limiting the observation period to 10 ka until the present. We show that the recovery is successful in all cases if the target parameter values are properly sampled by the initial ensemble probability distribution. This even includes cases in which the target viscosity values are located far in the tail of the initial ensemble probability distribution. Experiments show that the method is successful if enough near-field observations are available. This makes it work best for a period after substantial deglaciation until the present when the number of sea level indicators is relatively high.

Description: We use a fully coupled hydro-thermal model (TH) to quantify changes in the pore pressure and temperature distribution following the Last Glacial Maximum (LGM) in the intracontinental basins in Central and Northern Europe. We demonstrate that even without considering a direct mechanical coupling from the visco-elastic lithosphere rebound, the system is, at present-day, in a state of hydrogeologic and thermal disequilibrium as a result of the past ice sheet dynamics. We find that the local geology exerts an additional control on the subsurface response to imposed glacial loading, as evidenced by a contrasting thermal and pore pressure configuration in time and space. Highest rates of pore pressure dissipation are restricted to crustal domains that underwent substantial glacial loading, while the majority of the sedimentary sub-basins show a prominent signature of hydraulic disequilibrium (overpressure) at present. Groundwater-driven convective cooling and heating during the advance and retreat of the ice cap occurred mainly within sedimentary rocks, domains where thermal equilibration is ongoing. The spatial correlation between modeled pore pressure dissipation rates and postglacial uplift rates is indicative of a complex and transient hydrogeological system structurally connected to the viscous tail of the ongoing isostatic adjustment after the LGM, with important implications for assessing the long-term mechanical stability of this intraplate setting.

Description: We provide a single file (exodus II format) that contains all results of the modeling efforts of the associated paper. This encompasses all structural information as well as the pore pressure, temperature, and fluid velocity distribution through time. We also supply all files necessary to rerun the simulation, resulting in the aforementioned output file. The model area covers a rectangular area around the Central European Basin System (Maystrenko et al., 2020). The data publication is compeiment to Frick et al., (2021). The file published here is based on the structural model after Maystrenko et al., (2020) which resolves 16 geological units. More details about the structure and how it was derived can be found in Maystrenko et al., (2020). The file presented contains information on the regional variation of the pore pressure, temperature and fluid velocity of the model area in 3D. This information is presented for 364 time steps starting from 43,000 years before present and ending at 310000 years after present.

Description: Viscoelastic deformations of an earth structure in response to a time-varying surface load are analyzed in glacial isostatic adjustment (GIA). When solving this problem, aspects like flexure of the lithosphere and retarded response of mantle material become evident. Quantified are these by flexural rigidity and relaxation times. The concepts partly lose their relevance when changing from a 1D earth structure (only radial variations) to a 2D or a 3D earth structure (lateral variations). In regions like Fennoscandia and Laurentide, which are affected by GIA, lateral variations of the lithosphere and mantle structure are moderate and, so, the application of a 1D earth structure is widely accepted. But, also for these two regions one has to keep in mind that the respective 1D earth structures differ and that such an approximation mainly holds in the central part of the respective region. In contrast, lateral variations or a local structure of different viscosity have to be considered in areas like Patagonia, Antarctica or Alaska which is located above tectonic activity or covers a region with significant lateral changes in earth structure. But, already for the two former examples one has to keep in mind that the respective 1D earth structures inferred from GIA modelling differ between the two regions. Focusing on the relaxation behavior and the mantle-material transport, we discuss the effect of lateral variations on the deformation process. We will assess to which extent a 1D earth structure can represent lateral variability in structural features, and, at which point a 3D earth structure has to be considered. Such questions are of concern, when discussing GIA for geodetic applications as well as in earth system modeling as this study contributes to the climate modeling initiative Palmod.

Description: Ocean tide loading (OTL) and ocean tide dynamics (OTD) are known to be affected by Earth's internal structures, with the latter being affected by the self-attraction and loading (SAL) potential. Combining the 3D earth models Lyon and LITHO1.0, we construct a hybrid model to quantify the coupled effect of sediments, oceanic and continental lithosphere, and anelastic upper mantle on OTL and OTD. Compared to PREM, this more realistic 3D model produces significantly larger vertical OTL displacement by up to 3.9, 2.6, and 0.1 mm for the M2, K1, and Mf OTL, respectively. Moreover, it shows a smaller vector difference of 0.1 mm and a smaller amplitude difference of 0.2 mm than PREM with OTL observations at 663 Global Navigation Satellite System stations, a confirmation of the cumulative effect due to these earth features. On the other hand, we find a resonant impact of wider extent and larger magnitude on OTD, especially for the M2 and K1 tides. Specifically, this impact is concentrated in the ranges 0–6 mm and 0–1.5 mm for M2 and K1, respectively, which is considerably larger than the impact on SAL (mostly in the ranges 0–2 mm and 0–1.0 mm, respectively). Since the effect on vertical displacement is at a similar level compared to the accuracy of modern data-constrained ocean tide models that require correction of the geocentric tide by loading induced vertical displacements, we regard its consideration to be potentially beneficial in OTD modeling.

Description: Glacial-isostatic adjustment (GIA) models simulate the viscoelastic response of the solid earth due to loading. During the last glacial maximum, large areas in the northern and southern hemisphere were covered by km-thick ice sheets. Although most of the ice has been melted already 8,000 year ago, the time-delayed response of the viscoelastic earth is still a significant contribution to present-day uplift rates. The implementation of GIA models in global climate models is an essential part of the current research. Hereby, the choice of an appropriate earth structure in the GIA model plays an important role and has to be constrained by observational data. Here, we apply present-day uplift data to constrain a set of GIA models that differ in 3D earth structure. To this end, these different GIA models are validated against GPS uplift rates provided by Schumacher et al. (2019). The GPS stations are globally distributed and not necessarily clustered in regions with strong GIA signal. For validation, regions with the largest gradient present in the GIA signal are most crucial. Thus, we use a weighting scheme, where those GPS stations get a higher weight that are less correlated to all other stations. Additionally, uncertainties in the GPS rates appear due to the length of the GPS time series and due to station specifics such as the used GPS receiver, and are provided together with the rates as standard deviations. Thence, the weighting used for the validation is the sum of the correlation derived weights and the uncertainty derived weights. With this weighting in place, different GIA models can be validated against present day uplift rates by means of root mean square errors or mean absolute error.

Description: The interaction between ice sheets and the solid Earth plays an important role for ice-sheet stability and sea-level change and hence for global climate models. Glacial-isostatic adjustment (GIA) models enable simulation of the solid Earth response due to variations in ice-sheet and ocean loading and prediction of the relative sea-level change. Because the viscoelastic response of the solid Earth depends on both ice-sheet distribution and the Earth’s rheology, independent constraints for the Earth structure in GIA models are beneficial. Seismic tomography models facilitate insights into the Earth’s interior, revealing lateral variability of the mantle viscosity that allows studying its relevance in GIA modeling. Especially, in regions of low mantle viscosity, the predicted surface deformations generated with such 3D GIA models differ considerably from those generated by traditional GIA models with radially symmetric structures. But also, the conversion from seismic velocity variations to viscosity is affected by a set of uncertainties. Here, we apply geodynamically constrained 3D Earth structures. We analyze the impact of conversion parameters (reduction factor in Arrhenius law and radial viscosity profile) on relative sea-level predictions. Furthermore, we focus on exemplary low-viscosity regions like the Cascadian subduction zone and southern Patagonia, which coincide with significant ice-mass changes.

Description: The Antarctic Ice Sheet rests on a bed that is characterized by tectonical activity and hence by a heterogeneous rheology. Spots of extremely weak lithosphere structure could have strong impacts on the Glacial Isostatic Adjustment and hence on the stability of the ice sheet, possibly also for confined glacier regions and on timescales of decades down to even years (Barletta et al., 2018). We coupled the VIscoelastic Lithosphere and MAntle model (VILMA) to the Parallel Ice Sheet Model (PISM) and ran simulations over the last two glacial cycles. In this framework, VILMA considers both viscoelastic deformations of the solid Earth and gravitationally consistent mass redistribution in the ocean by solving for the sea-level equation (Martinec et al., 2018). In turn, PISM interprets this as a vertical shift in bed topography that directly affects the stress balance within the ice sheet and hence the grounding line dynamics at the interface of ice, ocean and bedrock. Here we present first results of the coupled Antarctic glacial-cycle simulations and investigate technical aspects, such as optimal coupling time steps, iteration schemes and convergence, for both one-dimensional and three-dimensional Earth structures. This project is part of the German Climate Modeling Initiative, PalMod2.

Description: We suggest to apply data assimilation in glacial isostatic adjustment (GIA) to constrain the mantle viscosity structure based on sea level observations. We apply the Parallel Data Assimilation Framework (PDAF) to assimilate sea level data into the time-domain spectral-finite element code VILMA in order to obtain better estimates of the mantle viscosity structure. In a first step, we reduce to a spherically symmetric earth structure and prescribe the glaciation history. A particle filter is used to propagate an ensemble of models in time. At epochs when observations are available, each particle's performance is estimated and the particles are resampled based on their performance to form a new ensemble that better resembles the true viscosity distribution. Using this algorithm, we show the ability to recover mantle viscosities from a set of synthetic relative sea level observations. Those synthetic observations are obtained from a reference run with a given viscosity structure that defines the target viscosity values in our experiments. The viscosity estimation is applied to a three-layer model with an elastic lithosphere and two mantle layers, and to a multi-layer model with a smoother viscosity profile. We use various subsets of realistic observation locations (e.g. only observations from Fennoscandia) and show that it is possible to obtain the target viscosity values in those cases. We also vary the time from which observations are available to evolve the test cases towards a realistic scenario for the availability of relative sea level observations. The most relevant cases start at 26.5ka BP and at 10ka BP as they mark the beginning of the maximum glaciation and the end of deglaciation with a larger amount of observations following, respectively, and end at present day.

Description: The elastic response of solid earth to glacier and ice sheet melting, the most important consequences of climate change, is a contemporaneous uplift. Here, we use interferometric synthetic aperture radar (InSAR) measurements to detect crustal deformation and mass loss near the Helheim glacier, one of the largest glaciers in southeastern Greenland. The InSAR time series of Sentinel-1 data between April 2016 and July 2020 suggest that there is a maximum cumulative displacement of ~6 cm in the line of sight (LOS) direction from the satellite to the ground near Helheim. We use an exponentially decreasing model of the thinning rate, which assumes that the mass loss starts at the lower-elevation terminal region of the glacier and continues to the higher-elevation interior. A linear inversion of the derived crustal uplift in the vicinity of bedrock using this model for surface loading in an elastic half-space suggests a mass loss of 8.33 Gt/year, which agrees with the results from other studies.